The yearly sales (in thousand units) of a product are given below.
| Year | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 |
| Sales (in thousand units) | 29 | 37 | 36 | 42 | 41 | 49 |
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | The first 3-year moving average | (I) | 36 |
| (B) | The first 4-year moving average (before centring) | (II) | 37.5 |
| (C) | The first 4-year centred moving average | (III) | 37 |
| (D) | The first 5-year moving average | (IV) | 34 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
Each moving average is the mean of a group of consecutive values, starting from the first year.
(A) The first 3-year moving average
This matches (IV) 34. It is placed against 2020.
\( \displaystyle \frac{29 + 37 + 36}{3} = \frac{102}{3} = 34 \)
(B) The first 4-year moving average (before centring)
This matches (I) 36. It lies between 2020 and 2021.
\( \displaystyle \frac{29 + 37 + 36 + 42}{4} = \frac{144}{4} = 36 \)
(C) The first 4-year centred moving average
This matches (II) 37.5. The second 4-year moving average is
\( \displaystyle \frac{37 + 36 + 42 + 41}{4} = \frac{156}{4} = 39 \)
Centring the first two averages places the result against 2021:
\( \displaystyle \frac{36 + 39}{2} = 37.5 \)
(D) The first 5-year moving average
This matches (III) 37. It is placed against 2021.
\( \displaystyle \frac{29 + 37 + 36 + 42 + 41}{5} = \frac{185}{5} = 37 \)